Higgs bundles over elliptic curves for real groups

The first author was supported by Fundacao de Amparo a Pesquisa do Estado de Sao Paulo through FAPESP 2012/16356-6 and BEPE-2015/06696-2. The second author was partially supported by the Ministerio de Economia y Competitividad of Spain through Project MTM2010-17717 and Severo Ochoa Excellence Grant.